In a binary communication system a 1 is transmitted by sending a +1 volt pulse and a 0 is transmitted by sending a −1 volt pulse. at the receiver the transmitted pulse is added with a noise z which has a gaussian distribution with z ∼ n (0, 1). in other words, if x is transmitted (x can be ±1 volts) we receive y = x + z. the receiver compares y with zero, if y > 0 it declares that a 1 was sent and if y ≤ 0 is declares that a 0 was sent. a. suppose that the receiver decides a 0 was sent if y< 0, and a 1 was sent if y> =0. what is the probability that the receiver makes an error given that a+1 was transmitted? a-1 was transmitted? b. what is the overall probability of error?

In may you used 400 kilowatt-hours of energy for electricity. a. calculate the total electrical energy use in joules. b. calculate your average power use in watts. c. assume that your power supplier generates electricity by burning oil. note that 1 liter of oil releases 12 million joules of energy. how much oil is needed to generate the electricity you use? give your answer in both liters and gallons. a. the total electrical energy use was nothing _ joules. (type an integer or a decimal.) b. the average power use is nothing _ watts. (round to the nearest whole number as needed.) c. to generate the electricity you used, nothing _ l is needed. (round to the nearest whole number as needed.) to generate the electricity you used, nothing _ gal is needed. (round to two decimal places as needed.)